Past exam of the mathematics course of the University of Cambridge / 2009 / iii / Paper 41 / 1 / b / Solution

Specify the expected control-group event probability at the chosen follow-up time, the intervention probability or smallest clinically important absolute reduction to detect, the primary test's significance level and whether it is one- or two-sided, the desired statistical power, and the allocation ratio. Statistical power is the probability of rejecting the null hypothesis under that specified alternative; its complement is the Type II error probability.

For two independent binary-outcome groups, these probabilities determine the response variances needed by the sample-size calculation. Also specify how much loss to follow-up is anticipated when converting the required evaluable sample into a recruitment target. Here the design is balanced and the stated primary significance level is $0.05$. A target statistical power such as $80\%$ or $90\%$ and the anticipated event probabilities cannot be recovered from the sample size alone, so they should not be invented. The recruitment inflation allows for attrition rather than changing the target effect.